Title: Testing and the Method of Sieves
Authors: Peter Bickel, Ya'acov Ritov and Thomas Stoker
Date: July, 1998
Pub: PDF
Url: http://www.stat.berkeley.edu/~bickel/brs798.pdf
Abstract:
This paper develops test statistics based on scores for the specification
of regression in nonparametric and semiparametric contexts.  We study
how different types of test statistics focus power on different directions
of departure from the null hypothesis.  We consider index models as basic
examples, and utilize sieves for nonparametric approximation.  We examine
various goodness-of-fit statistics, including Cramer-von Mises and
Kolmogorov-Smirnov forms.  For a "box-style" sieve approximation, we
establish limiting distributions of these statistics.  We develop a bootstrap
resampling method for estimating critical values for the test statistics,
and illustrate their performance with a Monte Carlo simulation.